The correct answer is option 4, Dinabandhu Mitra.

Option 1, Reverend James Long, is not the correct answer. He was an English Baptist missionary and scholar who was active in India during the 19th century. He is known for his work on Indian languages and literature, but he is not the author of Neel DarpUn.

Option 2, Michael Madhusudan Dutta, is also not the correct answer. He was a renowned Bengali poet and dramatist, but he did not write Neel DarpUn. Dutta is best known for his epic poem "Meghnad Badh Kavya" and his contributions to Bengali literature.

Option 3, Raja Ram Mohan Roy, is not the correct answer either. He was a social reformer and the founder of the Brahmo Samaj, a socio-religious movement in India. Although Roy played a significant role in Indian history, he did not write Neel DarpUn.

Therefore, the correct answer is option 4, Dinabandhu Mitra. He was a prominent Bengali playwright and poet who wrote Neel DarpUn, which was published in 1860.